0 Visualizing Volumes

My calculus class is working on volumes of revolution. I have found that success with this particular topic is related to a student's ability to visualize in three dimensions. I always have a few who struggle with that.

Fast forward to last week. I was shopping, and I found these on clearance:

For decorative use only. I am such a rule-breaker.

I traced out the shape of the region I wanted to rotate.

Cut it out. Open it up. Voila!

You have to hold it a certain way or it will sort of fall apart, but I thought it was a nice visual and tactile representation of a volume of rotation.

This one fell apart when I opened it up. I learned that you have to make sure some of the original glue is left intact when you cut out your shape. I tried running a bead of glue along one side, but then it wouldn't open very well.

Another drawback is that the semi-circular shape of the original pieces is somewhat limiting. I am sure these must be made in other shapes? I am going to raid a party store before we get to this topic again next year.

Still, my students were really intrigued to see what would happen as we cut and unfolded each one.

This one turned out really nice:

Happy rotating!